Three pipes, A, B, C can fill an empty cistern in 2, 3 and 6 hours respectively. They are opened together. After what time should B be closed, so that the cistern gets filled in exactly 1 hr 15 min?

Let capacity of cistern = L.C.M. (2,3,6) = 6 litres

A can fill it in 2 hours, => A's efficiency = $$\frac{6}{2}=3$$ litres/hr

Similarly, B's efficiency = $$2$$ litres/hr and C = $$1$$ litre/hr

Let B is opened for $$t$$ hours and A and C for $$\frac{5}{4}$$ hours

Acc to ques, => $$(3+1)\times\frac{5}{4}+2t=6$$

=> $$5+2t=6$$

=> $$2t=6-5=1$$

=> $$t=\frac{1}{2}$$ hour

$$\therefore$$ B should be closed after 30 min.

=> Ans - (A)